Jan 29 (Reuters) - Peabody Energy Corp reported a $1billion loss for the fourth quarter and warned of acurrent-quarter loss but said lower costs and a rebound inprices for steel-making coal would help lift its earnings as theyear progresses.

Peabody, the world's largest private sector coal miner, saidit expected earnings to rise due to higher volumes and prices atits Australian mines as well as lower production costs.

Shares of the company, valued at $6.75 billion, rose nearly6 percent to $26.64 in early trade on Tuesday. The stock hasfallen 35 percent since touching a year-high of $38.96 inFebruary to Monday's close.

The company expects an adjusted loss of between 4 cents and26 cents per share in the first quarter. Analysts on averagewere expecting a loss of 9 cents per share, according to ThomsonReuters I/B/E/S.

Peabody warned in December that its earnings would hit atrough in the first quarter due to higher costs in Australia,lower prices for metallurgical, or steel making, coal and a fallin sales and pricing in the United States.

But the company remained optimistic about the rest of 2013.

Peabody expects a 40 to 60 million ton increase in U.S. coaldemand, with the rise in natural gas prices prompting electricutilities to switch back to coal.

Thermal coal prices, however, remain weak, and Peabodyexpects U.S. revenue per ton to fall between 5 percent and 10percent from 2012 levels.

Benchmark thermal-coal price declined about 3percent to close at $87.15 in the three months ended Dec. 31.

Met coal prices, on the other hand, are expected to bounceback this year on strengthening steel prices in China.

"Turning to 2013, recent data suggests that China's economicgrowth is again accelerating, and we have seen some rebound inglobal coal prices," said Chief Executive Gregory Boyce.

Peabody is targeting sales of 230 million to 250 milliontons for the year, compared with 248.5 million tons in 2012.

SWINGS TO A LOSS

Peabody recorded pre-tax asset impairment charges totaling$884 million in the fourth quarter. The company said pricedeclines were a factor in writing down the value of certainAustralian operations and other non-core assets.

Peabody reported a net loss of $3.78 per share, comparedwith a net income of $222.4 million, or 82 cents per share, ayear earlier.

The adjusted loss was $1.12 per share, Peabody said.

The company said it had modified the definition of adjustedEBITDA (earnings before interest, taxes, depreciation andamortization), continuing operations, and diluted EPS to excludeasset impairment and mine closure costs.

At least two analysts said the company reported abetter-then-expected profit with adjusted earnings of 36 centsper share.

"Q4 was a nice beat versus our estimates, driven by a strongperformance of Peabody's Australian platform, where bothrealized prices and costs per ton came in better than we hadexpected," said Lucas Pipes of Brean Murray & Carret.

Analysts on average had expected earnings of 25 cents pershare, according to Thomson Reuters I/B/E/S.